Depp originally revealed plans to update the 1934 noir classic with his Pirates of the Caribbean: On Stranger Tides director Rob Marshall in 2010, with the production confirmed a year ago.
According to Deadline, Warner Bros has put a halt to production on the remake, in part because Depp is keen to take a break between films.
Reportedly the delay is also partially due to budgetary concerns. Production had been due to start in November, but will now likely be pushed back.
Several actresses including Emma Stone, Carey Mulligan and Rachel Weisz were reportedly vying to play the role of Nora opposite Depp.
Based on Dashiell Hammett's iconic detective novel, The Thin Man centres on Nick Charles (played by William Powell in the original film), a married man who solves murder mysteries alongside his wife Nora.
On Stranger Tides aside, Marshall has directed the big-screen musicals Nine and Chicago.
Watch a trailer for Pirates of the Caribbean: On Stranger Tides below: